. 109. OF THE CONNEXION OF FORMS. 109 



obtained will be a rhombohedron, which is more obtuse 

 than the given one. 



The inclined diagonals of this more obtuse rhombohedron, 

 assume the situation of the terminal edges of the other ; 

 while the horizontal projections of both are parallel. One 

 of these forms is said to be in a transverse position towards the 

 other, because this position may be obtained, by turning 

 a rhombohedron from its original position, round the prin- 

 cipal axis, for an angle of 60 or 180. If a rhombohedron is 

 in the transverse position towards another, it may be brought 

 into the parallel position, only by turning it again round 

 the axis for the same quantity. 



In the parallel position, a plane through the axis, and 

 the inclined diagonal, or the terminal edge of one rhom- 

 bohedron, passes at the same time through the inclined dia- 

 gonal or the terminal edge of the other ; in the transverse 

 position, on the contrary, the plane through the axis and 

 the inclined diagonal of the one at the same time passes 

 through the terminal edge of the other rhombohedron. 



In order to invert the process of derivation given above, 

 draw the inclined diagonals upon the faces of the rhombo- 

 hedron, and take away, by planes passing through every two 

 adjacent diagonals, those parts of the form which lie on 

 their outside. The remainder is the more acute rhombo- 

 hedron, from which the given one in its due position may be 

 derived according to the first method of derivation, as em- 

 ployed above. 



. 109- RATIO OF THE DERIVED RHOMBOHEDRONS. 



The axis of the rhombohedron, whose faces 

 touch the terminal edges of another, is to the 

 axis of this rhombohedron == J : 1 ; and the axis 

 of the rhombohedron whose terminal edges are 

 touched by the planes of another, is to the axis of 

 this in the ratio of 2 : 1 ; the horizontal projections 

 always being supposed equal. 



